I completely understand the frustration with Congress. The main obstacle there is the filibuster in the Senate, and the simple fact of the matter is that there was zero chance Manchin and Sinema would ever be willing to kill the filibuster over something like the Equality Act (something which Biden has routinely urged Congress to pass, I'd add).
At the end of the day, there's really only so much that can be done given the structure of the American government. The federal government's authority to interfere with state laws is quite limited, particularly under this Supreme Court, and structural biases in the government make it much much easier for Republicans to stop something than it is for Democrats to do something, all while Republican state governments can act freely at the level of their state. Oftentimes, there's isn't some magical hidden 'play dirty' lever that Democrats could easily pull but refuse to. Short of simply holding a gun up to his face, Biden literally could not make Manchin vote any particular way (and I'm sure he wanted to several times). Despite that, the Respect for Marriage Act was still a genuinely strong legislative achievement.
And to be clear, I don't mean to invalidate your frustration or say that any of this situation is right. But ultimately, there are reasons the mess is the way it is, and if we want to move things in a positive direction, we have to understand the rules and know what the available moves actually are.
Lastly, I'd add that the Biden White House, particularly the DoJ, has genuinely done quite a lot in order to enforce LGBT protections wherever they legally can, including routinely interpreting discrimination by sex to be inclusive of gender identity. Here's a general timeline: